Multiple-Point Modeling of Clay Lenses & the Impact on Aquifer ...pangea.stanford.edu/departments/ere/dropbox/scrf/documents/reports/… · Multiple-Point Modeling of Clay Lenses

Motivation Geology Geophysics Geostatistics Flow Simulation

Multiple-Point Modeling of Clay Lenses & theImpact on Aquifer Vulnerability

Whitney Trainor and Jef Caers

22nd SCRF Meeting

May 1, 2009

Whitney Trainor and Jef Caers: 22nd SCRF Meeting

Multiple-Point Modeling of Clay Lenses & the Impact on Aquifer Vulnerability


Goal: Develop a methodology that quantifies the Value ofInformation (VOI) of geophysical data for groundwatermanagement

• Decision-based

• Flow simulation models

• Geostatistics: methods for integrating geophysical data

• Demonstrate importance of data for groundwater modeling




Arhus Dataset

modified from Jorgensen, et al, 2003

I Geology:Glacial Buried Valleys

I Geophysics:Time-Domain Electromagnetic(TEM)

I Flow Simulation:Aquifer Vulnerability toSurface-born Contaminants

I Decision:Move farms or restrict urbandevelopment at zones of recharge




Glacial Erosion and Deposition

Network of Buried Valleys

(Jorgensen & Sanderson, 2006)

I “Waxing and wanning ofPleistocene ice sheets”BurVal Working Group, 2006

I Multi-generational glacialvalleys

I Cross-cut oldergenerations

I Can abruptly end







Cross Sectional View

modified from (Thomsen, Sondergaard, & Sorensen 2004)







Cross Sectional ViewSand: ρ > 60 ohm-mClay: ρ < 40 ohm-m

modified from (Thomsen, Sondergaard, & Sorensen 2004)




Time-Domain Electromagnetics (TEM)

NC Division of Water Resources

Tx - Transmitter loop (40m×40m)

Rx - Receiver loop (10m×10m)

σ - conductivity of layered earth





Tx - Transmitter loop (40m×40m)

Rx - Receiver loop (10m×10m)

σ - conductivity of layered earth





I Constant current Iwire

produces primary magneticfield Hp

∇× Hp = Iwire

I Current turned-off; changingmagnetic field inducessecondary electric field Es inthe earth∇× Es =

−∂(µHp)∂t





I Constant current Iwire

produces primary magneticfield Hp

∇× Hp = Iwire

I Current turned-off; changingmagnetic field inducessecondary electric field Es inthe earth∇× Es =

−∂(µHp)∂t





Es produces the image current It

It = σEs

It diffuses outward and downwardover time (t). Diffusion rate:

I is proportional to 1/sqrt(t)

I depends on earthconductivity (σ)





Es produces the image current It

It = σEs

It diffuses outward and downwardover time (t). Diffusion rate:

I is proportional to 1/sqrt(t)

I depends on earthconductivity (σ)





The diffusing, time varyingcurrent It produces time varyingsecondary magnetic Hs field.

∂(∇× Hs)

∂t=∂Itdt






∂(∇× Hs)

∂t=∂Itdt






∂(∇× Hs)

∂t=∂Itdt





This decaying magnetic field Hs

produces time-varying voltage∇V in receiver coil Rx

∇V = −∫∂(µHs)

∂t· nds





TEM Inversions:

* 1D resistivity (ρ) model, unique toTx-Rx location

* Computationally demanding

* Assume homogeneous half-space

* Only partially account for changingvolume of support




How has TEM been used?

X-Section View





X-Section View





Map View





Map View









Hydraulic Conductivity




Geostatistical modeling with snesim

Deterministic Modeling of BuriedValleys

Buried ValleyNon-Valley

P(A|B , C )

where:A = “clay lens occurring”B = TEM models (ρ)C = geologic knowledge(training image)




Calibration

Calibration to Driller’s Log

> 3, 000 TEM




Calibration

Calibration to Driller’s Log

> 3, 000 TEM

⇒property of

consequence:permeability

⇒

> 700 Driller’s Logs

* subjective observations oflithology




Calibration

Likelihood

I 7 Collocated TEM &Driller’s Logs (within 25m)

I Likelihoodp(ρ|lithology)

I Changing TEMVolume support

I Error in Driller’s LogInterpretation

Original Likelihood




Calibration

Likelihood

I 7 Collocated TEM &Driller’s Logs (within 25m)


I Changing TEMVolume support

I Error in Driller’s LogInterpretation

Alternative Likelihood




Calibration

Likelihood to Probability


⇓I Posterior

p(lithology |ρ)

Original Soft Probability

Alternate Soft Probability




Calibration

Simulation of Clay Lenses with snesim

Training Images

P(A|B , C )





Calibration

Simulation of Clay Lenses with snesim

Training ImagesP(A|B , C )





Flow Response

Example Permeability Realization

Sand 1000mDClay 0.1 mDVertical Exaggeration x25

Simulation Time: 20 years

Grid Size: 143x91x50

Boundary Conditions:

I 61 Extraction Wells

I Rainfall

I Boundary Recharge

Tracer: Mass Conservation




Aquifer Vulnerability


Hydraulic connections from surface to aquifer

Surface Tracer- Log Concentration

Geobody Concept

Renard & Caers, 2008







Surface Tracer- Log ConcentrationGeobody Concept


















Vulnerability= # of concentration bodies intersecting wells









Vulnerability= # of concentration bodies intersecting wells





Vulnerability- Cross Section Results

TI 1

permeability

TI 5

permeability






TI 1

permeability

TI 5

permeability






TI 1 TI 5

I Fingering vs. Uniform Front

I Tracer within top 10 grid cells (40m)

I Information on near surface more consequential





Vulnerability vs Clay Lens Size





Vulnerability vs Clay Lens Size





Towards VOI





Conclusions & Future Work

I Strong trend of clay lens size & aquifer vulnerability

I TEM possibly more informative for clay lenses <25 grid cell2

I Near-surface information: Pulled Array Continuous ElectricalSounding (PACES); top 30m

I Address the TEM support

I Streamline simulation to speed up tracer simulation

I Stochastic simulation of the buried valley locations



Documents

Multiple-Point Modeling of Clay Lenses & the Impact on Aquifer ...pangea.stanford.edu/departments/ere/dropbox/scrf/documents/reports/… · Multiple-Point Modeling of Clay Lenses